@Jose
MySQL is designed to run as a server that is separate from the clients using the database. As such, you can use a MySQL database with a non-GPL program as they communicate via a network (it's a separate process). There is no dynamic linking so it's not a single program as per the GPL.
If you really want the database code to be internal to the program, then SQLite (public domain) is an option. However, if your database gets big, you're better off running a MySQL server, and accessing it via TCP/IP, even if it's on the same machine.
Hans